Intrinsic Gyrotropic Magnetic Current of Orbital Origin

In gyrotropic crystals, an oscillating magnetic field induces a charge response known as the gyrotropic magnetic current. While its conventional origin is attributed to magnetic field modified band energy and shift in the Fermi-surface, a recent study identified an additional spin-driven magnetic displacement contribution. Here, we complete the picture by identifying the orbital counterpart of the magnetic displacement current. Using a density-matrix formulation that incorporates both minimal coupling and spin-Zeeman interactions, we derive the electronic equations of motion in the presence of an oscillating magnetic field and uncover a previously unexplored orbital contribution to the wavepacket velocity. Physically, this contribution arises from the time variation of the magnetic-field induced charge polarization. In the low frequency transport regime, this mechanism becomes purely intrinsic. We illustrate this intrinsic gyrotropic current of orbital origin in the ${\cal P}{\cal T}$-symmetric antiferromagnet CuMnAs. We show that the intrinsic gyrotropic magnetic current reverses sign upon N\'eel vector reversal, establishing it as a direct probe of antiferromagnetic order in CuMnAs and other $\mathcal{PT}$-symmetric antiferromagnets.